Problem: $J$ $K$ $L$ If: $ KL = 5x + 5$, $ JK = 3x + 4$, and $ JL = 65$, Find $KL$.
Answer: From the diagram, we can see that the total length of ${JL}$ is the sum of ${JK}$ and ${KL}$ $ {JK} + {KL} = {JL}$ Substitute in the expressions that were given for each length: $ {3x + 4} + {5x + 5} = {65}$ Combine like terms: $ 8x + 9 = {65}$ Subtract $9$ from both sides: $ 8x = 56$ Divide both sides by $8$ to find $x$ $ x = 7$ Substitute $7$ for $x$ in the expression that was given for $KL$ $ KL = 5({7}) + 5$ Simplify: $ {KL = 35 + 5}$ Simplify to find ${KL}$ : $ {KL = 40}$